U.S. patent application number 10/566843 was filed with the patent office on 2006-09-14 for two-dimensional photonic crystal multiplexer/demultiplexer.
This patent application is currently assigned to SUMITOMO ELECTRIC INDUSTRIES, LTD.. Invention is credited to Yoshihiro Akahane, Takashi Asano, Susumu Noda.
Application Number | 20060204161 10/566843 |
Document ID | / |
Family ID | 34269454 |
Filed Date | 2006-09-14 |
United States Patent
Application |
20060204161 |
Kind Code |
A1 |
Noda; Susumu ; et
al. |
September 14, 2006 |
Two-dimensional photonic crystal multiplexer/demultiplexer
Abstract
An object of the present invention is to provide a
multiplexer/demultiplexer capable of preventing a decrease in
multiplexing/demultiplexing efficiency due to an error in
wavelength or due to a crosstalk with other wavelengths. A
two-dimensional photonic crystal having holes 22 cyclically
arranged is provided with an input waveguide 23 and an output
waveguide 24. Located between the two waveguides are two point-like
defects 25 and 26, each consisting of a region devoid of the holes
22. From the light including various wavelengths and propagating
through the input waveguide 23, the two point-like defects extract
a ray of light having a wavelength determined by the shape of the
point-like defects and introduce it into the output waveguide 24.
Compared with the case where there is only one point-like defect,
the above-described construction increases the values of the
wavelength spectrum of the extracted light at around the resonance
wavelength and decreases the values at the wavelength range far
from the resonance wavelength. Therefore, the increase in the
values of the wavelength spectrum at around the resonance
wavelength ensures that the light having the desired wavelength can
be extracted from the waveguide by a large amount even if the
wavelength of the light propagating through the waveguide is
erroneously shifted from the resonance frequency. Occurrence of
noises within a wavelength range far from the resonance wavelength
and extraction of light having the wavelengths of adjacent channels
are also suppressed.
Inventors: |
Noda; Susumu; (Uji-shi,
JP) ; Asano; Takashi; (Kyoto-shi, JP) ;
Akahane; Yoshihiro; (Itami-shi, JP) |
Correspondence
Address: |
OLIFF & BERRIDGE, PLC
P.O. BOX 19928
ALEXANDRIA
VA
22320
US
|
Assignee: |
SUMITOMO ELECTRIC INDUSTRIES,
LTD.
5-33, Kitahama 4-chome, Chuo-ku
Osaki-shi
JP
541-0041
|
Family ID: |
34269454 |
Appl. No.: |
10/566843 |
Filed: |
August 24, 2004 |
PCT Filed: |
August 24, 2004 |
PCT NO: |
PCT/JP04/12114 |
371 Date: |
February 2, 2006 |
Current U.S.
Class: |
385/1 |
Current CPC
Class: |
G02B 6/1225 20130101;
G02B 6/12007 20130101; B82Y 20/00 20130101 |
Class at
Publication: |
385/001 |
International
Class: |
G02F 1/01 20060101
G02F001/01 |
Foreign Application Data
Date |
Code |
Application Number |
Aug 29, 2003 |
JP |
2003307654 |
Claims
1. A two-dimensional photonic crystal multiplexer/demultiplexer,
which is characterized by: a) a slab-shaped body; b) a plurality of
areas arranged in a lattice pattern with a predetermined cycle
within the body, where a refractive index of the aforementioned
areas differs from that of the body; c) a first optical
input/output section consisting of a waveguide formed in the body,
where the waveguide is made of a linear defect of the modified
refractive index areas; d) a second optical input/output section
formed in the body; and e) two or more point-like defect resonators
composed of point-like defects having substantially the same
resonance wavelength and arranged in series between the first and
second optical input/output sections, each point-like defect
consisting of a point-like region devoid of the modified refractive
index areas.
2. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 1, which is characterized in that the second
optical input/output section is a point-like defect whose Q-value
with respect to an outside of the crystal is smaller than that of
the point-like defect resonators.
3. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 2, which is characterized in that at least one
of the point-like resonators is a donor type defect formed by
eliminating one or more of the modified refractive index areas.
4. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 1, which is characterized in that the second
optical input/output section is a waveguide consisting of a linear
defect of the modified refractive index areas.
5. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 4, which is characterized in that the second
optical input/output section is provided with a second reflecting
section for reflecting light whose wavelength equals to the
aforementioned resonance wavelength.
6. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 1, which is characterized in that the first
optical input/output section is provided with a first reflecting
section for reflecting light whose wavelength equals to the
aforementioned resonance wavelength.
7. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 5, which is characterized in that: the body is
composed of plural forbidden band zones, with modified refractive
index areas being formed within each forbidden band zones with a
different arrangement cycle; the first optical input/output section
or the second optical input/output section is formed so that it
passes through all the forbidden band zones; and the resonance
wavelength of the point-like defect resonators falls within a
transmission wavelength band of the waveguide of the first or
second optical input/output section in a forbidden band zone
including the point-like defect resonators, whereas it is out of
the transmission wavelength band of the waveguide in any other
forbidden band zone.
8. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 1, which is characterized in that: there are two
point-like defect resonators; and the two point-like defect
resonators and the two optical input/output sections are
symmetrically arranged with respect to a point.
9. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 1, which is characterized in that one or more of
the modified refractive index areas located in a proximity of the
point-like defect resonators are shifted from positions determined
by the aforementioned arrangement cycle.
10. The two-dimensional photonic crystal multiplexer/demultiplexer
according to claim 1, which is characterized in that a coupling
ratio defined as
.mu..sup.2/[(.omega..sub.0/2).times.(1/Q.sub.in+1/Q.sub.v)].sup.2
is 0.2.about.10, where .omega..sub.0 is a resonance frequency of
the point-like defect resonators, Q.sub.in is a Q-value between the
point-like defect resonators and each of the first and second
optical input/output section, Qv is a Q-value between each of the
point-like defect resonators and an outside of the crystal, and
.mu. is a mutual coupling coefficient between two point-like defect
resonators.
Description
TECHNICAL FIELD
[0001] The present invention relates to a two-dimensional photonic
crystal multiplexer/demultiplexer used for wavelength division
multiplexing communication or other techniques. Particularly, it
relates to a technique for improving the
multiplexing/demultiplexing characteristics.
BACKGROUND ART
[0002] In recent years, the techniques used in wavelength division
multiplexing (WDM) transmission systems have made remarkable
progress. WDM is a technique for transmitting multiple pieces of
information by propagating plural wavelengths (or frequencies) of
light through a single transmission line, with each wavelength of
light carrying a different signal (Note: the term "light" used in
this specification includes electromagnetic waves). This technique
requires an optical multiplexer and an optical demultiplexer, or
wavelength filters, for mixing multiple wavelengths of light at the
inlet of the transmission line and then separating the mixed light
into each wavelength of light at the outlet. An example of
conventional demultiplexers is arrayed waveguide grating. However,
to adequately decrease the loss of light, arrayed waveguide
gratings currently used are somewhat oversized, as large as roughly
several square centimeters.
[0003] To increase the capacity of the transmission system and
reduce the size of the devices used in it, developments of
multiplexers, demultiplexers and wavelength filters using photonic
crystals are underway. A photonic crystal is a functional material
having a cyclic distribution of refractive index, which provides a
band structure with respect to the energy of light. This device is
particularly featured in that it has an energy region (called the
photonic bandgap) that does not allow the propagation of light.
Introduction of an appropriate defect into the distribution of
refractive index in the photonic crystal creates an energy level
(called the defect level) due to the defect within the photonic
bandgap. This allows only a specific wavelength of light having an
energy corresponding to the defect level to exist within the
wavelength range corresponding to the energy levels included in the
photonic bandgap. Forming a linear defect in the crystal provides a
waveguide, and forming a point-like defect in the crystal provides
a resonator. The shape of the defect determines a wavelength,
called the resonance wavelength, at which the resonance of light
takes place.
[0004] Non-Patent Document 1 discloses the result of a computer
simulation of a photonic crystal composed of infinitely long
cylindrical elements made of a high refractive index material and
arranged in a square lattice pattern. This construction allows
light to be controlled by the photonic bandgap within a plane
parallel to the square lattice. However, it does not enable the
control of light in the direction perpendicular to the
aforementioned plane. Photonic crystals having such a construction
are impractical.
[0005] Patent Document 1 discloses a photonic crystal having a
plate-shaped body in which plural areas having a refractive index
different from that of the body (called the "modified refractive
index area" hereinafter) are cyclically arranged to create a cyclic
distribution of refractive index. This construction can control
light within the body because a photonic bandgap is present within
the plane of the body and the difference in refractive index
between the body and the surrounding air confines light within the
body in the direction perpendicular to the body. In this
construction, a waveguide is formed by eliminating the modified
refractive index areas along a line ([0025], FIG. 1), and a
point-like defect is formed by eliminating the modified refractive
index areas within a point-like region ([0029], FIG. 1). As an
embodiment, Patent Document 1 shows a two-dimensional photonic
crystal having modified refractive index areas, each consisting of
a cylindrical hole, cyclically arranged in a triangular lattice
pattern, where the diameter of one of the cylindrical holes located
in the proximity of the waveguide is increased to be a point-like
defect.
[0006] [Non-Patent Document 1] S. Fan et al., "Channel Drop
Tunneling through Localized States", Physical Review Letters, (US),
American Physical Society, 1998, vol. 80, pp. 960-963
[0007] [Patent Document 1] Japanese Unexamined Patent Publication
No. 2001-272555 ([0025], [0029], FIG. 1)
[0008] This type of two-dimensional photonic crystal can function
as a demultiplexer for separating a ray of light whose wavelength
equals to the resonance wavelength of the point-like defect from
the light including plural wavelengths superimposed and propagating
through the waveguide, and for emitting the light through the
point-like defect to the outside. It can also function as a
multiplexer that introduces, from the outside of the crystal, a ray
of light whose wavelength equals to the resonance wavelength of the
point-like defect into superimposed light propagating through the
waveguide. Thus, one and the same two-dimensional photonic crystal
can function as a multiplexer and as a demultiplexer. Such a
two-dimensional photonic crystal is called the
"multiplexer/demultiplexer" in this specification. Creating plural
point-like defects having different shapes in the proximity of the
waveguide provides a multiplexer/demultiplexer in which each
point-like defect multiplexes or demultiplexes a ray of light
having a different wavelength. In the case where the plural
wavelengths of light each carries a different signal, it is
possible to extract a specific signal from the transmission line
(i.e. the waveguide) with the demultiplexer or introduce a specific
signal into the transmission line with the multiplexer.
[0009] In the above-described multiplexer/demultiplexer, the
point-like defect multiplexes or demultiplexes not only the ray of
light having its resonance wavelength, .lamda..sub.0, but also
other rays of light included within a certain wavelength range
around the resonance wavelength .lamda..sub.0 by certain
percentages. In the case of the above-described conventional
two-dimensional photonic crystal multiplexer/demultiplexer, the
multiplex/demultiplex spectrum takes the form of a Lorenz function
around the resonance wavelength .lamda..sub.0, as shown in FIG. 1.
A multiplex/demultiplex spectrum expressed by a Lorenz function has
a sharp peak; the value of the multiplex/demultiplex spectrum
rapidly falls as the distance from the resonance wavelength
.lamda..sub.0 increases, and it forms a long tail as the distance
becomes much larger. Such a multiplex/demultiplex spectrum
expressed by a Lorenz function is accompanied by two problems to be
solved with respect to the multiplexing/demultiplexing
operations.
[0010] The first problem results from the sharpness of the peak of
the multiplex/demultiplex spectrum. An aged deterioration or a
temperature change in the system used may cause an error in the
wavelength of light propagating through the waveguide or in the
resonance wavelength of the multiplexer/demultiplexer. This will
cause a discrepancy .delta..lamda. between the resonance wavelength
.lamda..sub.0 of the point-like defect (i.e. the peak wavelength of
the multiplex/demultiplex spectrum) and the wavelength
.lamda..sub.1 of the light propagating through the waveguide. As
can be understood from FIG. 1, even a very small discrepancy will
make the value of the multiplex/demultiplex spectrum at
.lamda..sub.1 considerably smaller than at .lamda..sub.0. This
means that even a slight change in the wavelength can deteriorate
the multiplexing/demultiplexing efficiency if the
multiplex/demultiplex spectrum is expressed by a Lorenz
function.
[0011] The second problem results from the long tail of the
multiplex/demultiplex spectrum. Presence of such a long tail will
allow rays of light having wavelengths far from .lamda..sub.0 to be
undesirably mixed, thus causing a noise. Also, the tail may overlap
the wavelength of the signal of an adjacent channel, causing a
crosstalk between the two signals.
DISCLOSURE OF THE INVENTION
Problems to be Solved by the Invention
[0012] Thus, the present invention intends to provide a
two-dimensional photonic crystal multiplexer/demultiplexer capable
of preventing the multiplexing/demultiplexing efficiency from
deteriorating due to an error of the input signal or the resonance
wavelength, and also suppressing the crosstalk caused by the tail
of the multiplex/demultiplex spectrum, each problem being
attributable to the peak shape of the multiplex/demultiplex
spectrum of each point-like defect.
Means for Solving the Problems
[0013] To solve the above-described problems, the present invention
provides a two-dimensional photonic crystal
multiplexer/demultiplexer, which is characterized by:
[0014] a) a slab-shaped body;
[0015] b) a plurality of areas arranged in a lattice pattern with a
predetermined cycle within the body, where the refractive index of
the aforementioned areas differs from that of the body;
[0016] c) a first optical input/output section consisting of a
waveguide formed in the body, where the waveguide is made of a
linear defect of the modified refractive index areas;
[0017] d) a second optical input/output section formed in the body;
and
[0018] e) two or more point-like defect resonators composed of
point-like defects having substantially the same resonance
wavelength and arranged in series between the first and second
optical input/output sections, each point-like defect consisting of
a point-like region devoid of the modified refractive index
areas.
[0019] The two-dimensional photonic crystal
multiplexer/demultiplexer according to the present invention has a
body consisting of a slab, or a thin plate whose size in the
in-plane direction is much larger than its thickness. This body is
provided with areas (i.e. the modified refractive index areas)
having a refractive index different from that of the body and being
arranged in a lattice pattern with a predetermined cycle. This
construction provides a two-dimensional photonic crystal having a
photonic bandgap that prevents rays of light within a specific
wavelength band determined by the aforementioned cycle from passing
through the body along the in-plane direction. Within the
two-dimensional photonic crystal having the above-described
structure, light is totally reflected at the boundary between the
body and the outside (e.g. the air) due to the difference in
refractive index between them. Thus, the light is prevented from
escaping from the body to the outside. Examples of the lattice
pattern for arranging the modified refractive index areas are
triangular lattice patterns and square lattice patterns. The
refractive index of the modified refractive index areas may be
higher or lower than that of the body. The modified refractive
index areas may be holes arranged in a cyclic pattern in the body.
This construction is preferable because it produces a large
difference in refractive index between the areas and the body.
Another point is that it is easy to manufacture.
[0020] The body is provided with a first optical input/output
section consisting of a waveguide made of a linear defect of the
modified refractive index areas. In a typical example, the
waveguide is formed by eliminating the modified refractive index
areas, or by omitting the modified refractive index areas, along a
line. The waveguide functions as an optical input section for
introducing light including plural wavelengths superimposed into
the demultiplexer if it is used as a demultiplexer, or as an
optical output section for extracting light including plural
wavelengths superimposed to the outside if it is used as a
multiplexer.
[0021] The body is also provided with a second optical input/output
section. This section functions as an optical output section for
extracting light having a specific wavelength to the outside of the
crystal if it is used as a demultiplexer, or as an optical input
section for introducing light having a specific wavelength into the
multiplexer if it is used as a multiplexer. The second optical may
be either a waveguide or a point-like defect. A second optical
input/output section taking the form of a point-like defect can be
formed by creating a point-like region devoid of the modified
refractive index areas. The point-like defect can be obtained by
making the size of one of the modified refractive index areas
different from that of the others or by eliminating one of these
areas. It is also possible to make the point-like defect composed
of two or more modified refractive index areas adjacent to each
other. In this case, the set of modified refractive index areas is
regarded as a single point-like defect. To extract light from the
crystal to the outside or introduce light into the multiplexer as
described earlier, it is desirable to make the Q-value between the
point-like defect and the outside of the crystal smaller than that
of the point-like defect resonators to be described later. Q-value
is an index that represents the performance of a resonator, which,
by definition, is inversely proportional to the percentage of the
amount of energy leaking from the resonators per unit of time.
Accordingly, a larger Q-value will reduce the amount of energy of
light leaking from the resonator. A second optical input/output
section taking the form of a waveguide can be formed by the same
method as used for forming the waveguide of the first optical
input/output section. It is also possible to add one or more
point-like defects in the proximity of the waveguide of the second
optical input/output section so that light can be extracted from
the waveguide via the point-like defect to the outside of the
crystal, or introduced into the multiplexer through the point-like
defect.
[0022] Between the first and second input/output sections, two or
more point-like defect resonators having substantially the same
resonance wavelength are arranged in series. For example, they can
be arranged along the direction perpendicular to the waveguide of
the first optical input/output section, along a direction at an
angle to the waveguide, or in a zigzag pattern. The point-like
defect resonators can be formed by the same method as used for
forming the point-like defect of the aforementioned optical
input/output section.
[0023] The point-like defect resonators, which do not directly
introduce or emit light from or to the outside, should be
preferably designed so that it allows only a small amount of light
to leak to the outside of the crystal. A donor type defect formed
by creating a region devoid of the modified refractive index areas,
or by omitting the modified refractive index areas, is more
suitable for the point-like defect resonators than an acceptor type
defect obtained by increasing the size of one of the modified
refractive index areas because the donor type yields a higher
Q-value (Q.sub.v) between each point-like defect resonator and the
outside of the crystal than that obtained with the acceptor type.
The value Q.sub.v can be further increased by shifting the modified
refractive index area within the proximity of the point-like defect
resonators from the position determined by the arrangement cycle.
Suppose that the point-like defect formed by eliminating three
modified refractive index areas located adjacent to each other on a
straight line. Then, Q.sub.v.about.5200 if there is no shift of the
modified refractive index areas, whereas Q.sub.v.about.45000 if two
modified refractive index areas located closest to the point-like
defect are shifted.
[0024] Light is transmitted between the first optical input/output
section and the point-like defect resonator closest to the first
optical input/output section, between each pair of adjacent
point-like defect resonators, and between the second optical
input/output section and the point-like defect resonator closest to
the second optical input/output section. The Q-value determined by
the components concerned and their distance will be an index of the
transmission of light.
[0025] The two-dimensional photonic crystal optical
multiplexer/demultiplexer constructed as described above functions
as either a multiplexer or a demultiplexer as follows. Firstly, the
operation of a demultiplexer for separating a ray of light having a
predetermined wavelength from light including plural wavelengths
superimposed is described. When the superimposed light is
propagated through the waveguide of the first optical input/output
section, the point-like defect resonator closest to the waveguide
traps only a ray of light whose wavelength equals to the resonance
wavelength of the point-like defect resonators from the
superimposed light. The trapped light is then successively captured
by the adjacent point-like defects and finally reaches the second
optical input/output section, which emits the light to the outside
of the crystal. In the case of a multiplexer, a ray of light whose
wavelength equals to the resonance wavelength of the point-like
defect resonators is introduced into the second optical
input/output section and then successively trapped by the
point-like defect resonators in the opposite order. The trapped
light finally reaches the waveguide of the first optical
input/output section, where it is mixed into the superimposed light
propagating through the waveguide.
[0026] The spectrum of the light multiplexed or demultiplexed by
the multiplexer/demultiplexer according to the present invention is
examined. This examination assumes that there are two point-like
defect resonators located between the two optical input/output
sections, as shown in FIG. 2A. For comparison, the
multiplex/demultiplex spectrum obtained with a conventional
multiplexer/demultiplexer having only one point-like defect
resonator between the two optical input/output sections, as shown
in FIG. 2B, is also examined.
[0027] In FIG. 2A, two point-like defect resonators 13 and 14, both
having a resonance wavelength .lamda..sub.0 and a resonance
frequency .omega..sub.0 (=2.pi.c/.lamda..sub.0, where c is the
speed of light), are located between a first optical input/output
section 11 consisting of a waveguide and a second optical
input/output section 12 consisting of another waveguide formed in
the same manner as the first one. Let Q.sub.in denote both the
Q-value between the first optical input/output section and the
point-like defect resonator closest to that section and the Q-value
between the second optical input/output section and the point-like
defect resonator closest to that section. Also, let Q.sub.v denote
the Q-value between each of the point-like defect resonators and
the outside of the crystal. The present analysis uses attenuation
constants .tau..sub.e and .tau..sub.0 defined as
.tau..sub.e=2Q.sub.in/.omega..sub.0 and
.tau..sub.0=2Q.sub.v/.omega..sub.0. The mutual coupling coefficient
between the two point-like defect resonators is denoted by .mu..
Letting a.sub.L and a.sub.R denote the amplitudes of the two
resonators observed under the condition that no waveguide is
present, .mu. can be derived from the following equations:
da.sub.L/dt=(j.omega..sub.0-1/.tau..sub.0)a.sub.L-j.mu.a.sub.R and
da.sub.R/dt=(j.omega..sub.0-1/.tau..sub.0)a.sub.R-j.mu.a.sub.L.
Using these parameters, a calculation based on the mode coupling
theory gives the multiplex/demultiplex spectrum I(.omega.) as
follows: I .times. .times. ( .omega. ) = 1 .tau. e 2 .mu. 2
.function. [ { ( 1 .tau. 0 + 1 .tau. e ) 2 + .mu. 2 } 2 + 2 .times.
.times. { ( 1 .tau. 0 + 1 .tau. e ) 2 - .mu. 2 } .times. ( .omega.
- .omega. 0 ) 2 + ( .omega. - .omega. 0 ) 4 ] ( 1 ) ##EQU1##
[0028] The conventional multiplexer/demultiplexer shown in FIG. 2B
has only one point-like defect resonator 17 between the first
optical input/output section 15 consisting of a waveguide and the
second optical input/output section 16 consisting of another
waveguide having the same structure. In this case, the
multiplex/demultiplex spectrum is calculated as follows: I .times.
.times. ( .omega. ) = 1 ( .tau. e .tau. 0 + 2 ) 2 + .tau. e 2
.function. ( .omega. - .omega. 0 ) 2 ( 2 ) ##EQU2##
[0029] Equation (2) is an expression of the Lorenz type
multiplex/demultiplex spectrum described earlier; it has a term of
frequency .omega..sup.2 in the denominator. In contrast, the
denominator in equation (1) includes an .omega..sup.4 term in
addition to an .omega..sup.2 term. Compared to the .omega..sup.2
term, the .omega..sup.4 term helps the value of the
multiplex/demultiplex spectrum to increase within a range close to
the resonance frequency .omega..sub.0 and decrease within a range
far from .omega..sub.0. As a result, in the
multiplexer/demultiplexer according to the present invention, the
multiplex/demultiplex spectrum takes (i) larger values within a
range close to .omega..sub.0 and (ii) smaller values within a range
far from .omega..sub.0, compared to that of the conventional
multiplexer/demultiplexer.
[0030] If .mu..sup.2=(1/.tau..sub.0+1/.tau..sub.e).sup.2, the
.omega..sup.2 term in the denominator in equation (1) equals to
zero, meaning that the .omega..sup.4 term works most
effectively.
[0031] FIGS. 3A and 3B each show examples of multiplex/demultiplex
spectrums: one expressed by equation (1) with
.mu..sup.2=(1/.tau..sub.0+1/.tau..sub.e).sup.2 and the other
expressed by equation (2). The solid lines correspond to equation
(1) and the broken lines correspond to equation (2). The abscissa
indicates the wavelength, and the ordinate indicates the
multiplex/demultiplex spectrum I(.lamda.) in decibels:
I.sub.dB=10.times.log[I(.lamda.)/I(.lamda..sub.0)]. The resonance
wavelength .lamda..sub.0 is 1550 nm. FIG. 3B is an enlarged view of
FIG. 3A. From the shapes of these multiplex/demultiplex spectrums,
it is clear that the two-dimensional photonic crystal optical
multiplexer/demultiplexer according to the present invention yields
the following effects: (i) The multiplex/demultiplex spectrum takes
larger values within a range close to .omega..sub.0. Even if the
frequency .omega..sub.1 of the light propagating through the
waveguide is shifted from the resonance frequency .omega..sub.0 for
some reason, such as an error in the wavelength of the light
propagating through the waveguide or an error of the resonator, the
multiplex/demultiplex spectrum maintains a large value at frequency
.omega..sub.1. Therefore, the multiplexing/demultiplexing
efficiency becomes higher than that of the conventional
multiplexer/demultiplexer. In case (i), the multiplex/demultiplex
spectrum becomes flattened at around the resonance frequency
.omega..sub.0, as shown in FIGS. 3A and 3B. In the following
description, the flattened shape of the multiplex/demultiplex
spectrum is referred to as the "flattop."
[0032] (ii) The multiplex/demultiplex spectrum takes smaller values
within a range far from .omega..sub.0. This prevents undesired
wavelengths of light from being mixed into the multiplexed or
demultiplexed light and thereby causing a noise. It also suppresses
the crosstalk caused by the overlapping of the signal frequency of
an adjacent channel.
[0033] For the multiplexer/demultiplexer, it is desirable that the
value of the multiplex/demultiplex spectrum at a frequency shifted
from the resonance frequency .omega..sub.0 by 0.005% is equal to or
larger than -1 dB (or 79%) of the value at .omega..sub.0. To
satisfy this condition, the ratio of .mu..sup.2 to
[(.omega..sub.0/2).times.(1/Q.sub.in+1/Q.sub.v)].sup.2, i.e.
.mu..sup.2/[(.omega..sub.0/2).times.(1/Q.sub.in+1/Q.sub.v)].sup.2,
should be preferably 0.2.infin.10. This ratio is called the
"coupling ratio" in this specification. If this ratio equals to
one, or if
.mu..sup.2=[(.omega..sub.0/2).times.(1/Q.sub.in+1/Q.sub.v)].sup.2,
the term of (.omega.-.omega..sub.0).sup.2 in the denominator of
equation (1) becomes zero, thus forming the most ideal flattop
shape.
[0034] The above-described model illustrated the case where there
are two point-like defect resonators and the second optical
input/output section is a waveguide. The aforementioned number may
be increased from two to N, in which case the term of
.omega..sup.2N will work in the same manner as in the case of the
previous model. If the distance between the first and second
optical input/output sections is large, it is advantageous to
provide more than two point-like defect resonators to connect the
two sections. If more than two point-like defect resonators are
used, it is necessary to individually design the point-like defect
resonators so that they have the same resonance frequency and the
same Q-value because each point-like defect resonator has a
different relationship with the surroundings. Similarly, if the
second optical input/output section is a point-like defect, it is
necessary to individually design the point-like defect resonators
because the relationship between each point-like defect resonator
and the surroundings changes due to the difference between the
second optical input/output section and the first optical
input/output section (i.e. a waveguide). If there are two
point-like defect resonators and the second optical input/output
section is a waveguide, it is preferable to symmetrically arrange
the two point-like defect resonators and the two optical
input/output sections with respect to a point. This arrangement
establishes the same relationship between each of the two
point-like defect resonators and the surroundings, allowing the use
of the same type of point-like defect resonators to obtain the same
resonance frequency and the same Q-value. This facilitates the
designing of the multiplexer/demultiplexer.
[0035] Even a ray of light whose wavelength equals to the resonance
wavelength of the point-like defect resonators can pass by the
point-like defect resonators by a certain percentage
(transmittance) without being introduced from the first optical
input/output section into the resonators. The light is also
reflected by the point-like defect resonators by a certain
percentage (reflectance). If the second optical input/output
section is a waveguide, the light propagates toward both ends of
the waveguide. Suppressing these phenomena will improve the
multiplexing/demultiplexing efficiency. Therefore, it is preferable
to provide the first input/output section and/or the second optical
input/output section with a reflecting section for reflecting light
whose wavelength equals to the resonance wavelength of the
point-like defect resonators. In the first optical input/output
section provided with the reflecting section, the light that has
not been introduced into the point-like defect resonators but has
passed by the resonators will be reflected by the reflecting
section and then introduced into the resonators. An appropriate
distance setting between the point-like defect resonators and the
reflecting section will cause a destructive interference between
the light reflected by the point-like defect resonators and the
light reflected by the reflecting section, thereby attenuating
them. Providing the second optical input/output section with the
reflecting section will allow the extraction or introduction of
light to be performed only at one end of the waveguide of the
second optical input/output section.
[0036] For example, the reflecting section can be constructed as
follows: Initially, the body is divided into plural zones (called
the "forbidden band zones"), with modified refractive index areas
being formed within each forbidden band zones with a different
arrangement cycle. Then, the first optical input/output section or
the second optical input/output section is formed so that it passes
through all the forbidden band zones. The transmission wavelength
band of the waveguide changes depending on the cycle of the
modified refractive index areas. Therefore, the cycle of each
forbidden band zone can be appropriately determined so that the
resonance wavelength of the point-like defect resonators falls
within the transmission wavelength band of the waveguide of the
first or second optical input/output section in a forbidden band
zone including the point-like defect resonators, whereas it is out
of the transmission wavelength band of the waveguide in any other
forbidden band zone. This construction prevents the light having
the resonance wavelength from propagating through the waveguide in
the other forbidden band zones; the light will be reflected at the
boundary between the forbidden band zone concerned and an adjacent
forbidden band zone. Thus, the boundary functions as the reflecting
section. A structure having plural forbidden band zones described
above is called the "heterostructure" in this specification.
[0037] FIG. 4 shows the first optical input/output section 11
having a first reflecting section 18 and the second optical
input/output section 12 having a second reflecting section 19. In
this case, the multiplex/demultiplex spectrum I(.omega.) is given
by: I .times. .times. ( .omega. ) = 4 .tau. e 2 .mu. 2 .function. [
{ ( 1 .tau. 0 + 1 .tau. e ) 2 + .mu. 2 } 2 + 2 .times. .times. { (
1 .tau. 0 + 1 .tau. e ) 2 - .mu. 2 } .times. ( .omega. - .omega. 0
) 2 + ( .omega. - .omega. 0 ) 4 ] ( 3 ) ##EQU3##
[0038] This spectrum is four times the previous one obtained in the
case where no reflecting section is present. Particularly, if
.mu..sup.2/=(1/.tau..sub.0+1/.tau..sub.e).sup.2 and
Q.sub.in<<Q.sub.v the multiplex/demultiplex spectrum at
.omega.=.omega..sub.0 equals to one, meaning that the
multiplexing/demultiplexing efficiency is 100%.
BRIEF DESCRIPTION OF THE DRAWINGS
[0039] FIG. 1 is an illustration for explaining problems relating
to the multiplex/demultiplex spectrum of a conventional
two-dimensional photonic crystal multiplexer/demultiplexer.
[0040] FIG. 2A is a schematic diagram of a two-dimensional photonic
crystal multiplexer/demultiplexer according to the present
invention, and FIG. 2B is another two-dimensional photonic crystal
multiplexer/demultiplexer as a comparative example having only one
point-like defect resonator.
[0041] FIGS. 3A and 3B are graphs showing an example of the
multiplex/demultiplex spectrum of a two-dimensional photonic
crystal multiplexer/demultiplexer according to the present
invention.
[0042] FIG. 4 is a schematic diagram of a two-dimensional photonic
crystal multiplexer/demultiplexer having a heterostructure.
[0043] FIG. 5A is a perspective view and FIG. 5B is a plan view of
an embodiment of the two-dimensional photonic crystal
multiplexer/demultiplexer according to the present invention.
[0044] FIG. 6 is a plan view for explaining the point-like defect
of the two-dimensional photonic crystal multiplexer/demultiplexer
of the aforementioned embodiment.
[0045] FIG. 7 is a schematic diagram of the two-dimensional
photonic crystal multiplexer/demultiplexer of the comparative
example.
[0046] FIG. 8 is a graph showing the result of calculating the
multiplex/demultiplex spectrums of the two-dimensional photonic
crystal multiplexers/demultiplexers of the aforementioned
embodiment and the comparative example, using the mode coupling
theory.
[0047] FIG. 9 shows the result of calculating the
multiplex/demultiplex spectrum of the two-dimensional photonic
crystal multiplexer/demultiplexer, using the finite difference time
domain (FDTD) method.
[0048] FIG. 10 is a plan view of a two-dimensional photonic crystal
multiplexer/demultiplexer as another embodiment.
[0049] FIG. 11 is a schematic diagram showing another embodiment of
the two-dimensional photonic crystal multiplexer/demultiplexer
according to the present invention.
[0050] FIG. 12 is a plan view of an embodiment of the
two-dimensional photonic crystal multiplexer/demultiplexer having a
heterostructure.
[0051] FIG. 13 is a chart showing the transmission wavelength band
of the waveguide of the two-dimensional photonic crystal
multiplexer/demultiplexer having a heterostructure.
EXPLANATION OF NUMERALS
[0052] 11, 15 . . . First Optical Input/output section [0053] 12,
16 . . . Second Optical Input/output section [0054] 13, 14, 17 . .
. Point-Like Defect Resonator [0055] 21 . . . Body [0056] 22 . . .
Hole [0057] 23, 65 . . . Input Waveguide [0058] 24, 66 . . . Output
Waveguide [0059] 25, 26, 31, 32, 51, 67, 68 . . . Point-Like
Defect
BSET MODE FOR CARRYING OUT THE INVENTION
[0060] FIG. 5A is a perspective view and FIG. 5B is a plan view of
an embodiment of the two-dimensional photonic crystal
multiplexer/demultiplexer according to the present invention. The
body 21, which is slab shaped, is provided with modified refractive
index areas created by boring holes 22 in a triangular lattice
pattern with cycle a. This body has an input waveguide 23 and an
output waveguide 24, each of which is formed by linearly
eliminating the holes 22, or omitting the formation of the holes
22, along a single line. Located between the input waveguide 23 and
the output waveguide 24 are two point-like defects 25 and 26
identically shaped. These point-like defects 25 and 26 will be
detailed later. The distances between the input waveguide 23 and
the point-like defect 25 and between the point-like defect 26 and
the output waveguide 24 each correspond to five lines of the holes
22: (5/2).times.3.sup.0.5a. The distance between the two point-like
defects 25 and 26 is 4.times.3.sup.0.5a. The following calculation
assumes that a is 420 nm and the diameter of the hole 22 is 240 nm.
In this two-dimensional photonic crystal multiplexer/demultiplexer,
the two point-like defects and the two waveguides are symmetrically
arranged with respect to a point.
[0061] As shown in FIG. 6, the point-like defects 25 and 26 are
each formed by omitting three holes 22 lying on a straight line.
Being entirely constituted by the same material as that of the body
21, these point-like defects can easily confine light because there
is a difference in refractive index between the body 21 and the
surrounding air. Therefore, these point-like defects prevent light
from leaking from the surface of the body 21 to the outside, thus
yielding a high level of Q-value. In addition, as shown in FIG. 6B,
two holes 221 and 222 closest to the point-like defects are each
shifted to a position 0. 15a farther from the point-like defect
than the position shown in FIG. 6A where each hole is located at a
triangular lattice point. According to calculation of the present
inventors, shifting the holes 221 and 222 as described above will
enhance Q.sub.v (the Q-value between the point-like defect and the
outside of the crystal) up to Q.sub.v.about.46600, much higher than
the value obtained without shifting the holes:
Q.sub.v.about.5200.
[0062] In addition to Q.sub.v.about.46600, the parameters relating
to the two-dimensional photonic crystal multiplexer/demultiplexer
of the present embodiment can be calculated using the finite
difference time domain method (FDTD method) as follows: Q.sub.in,
the Q-value between the input waveguide 23 and the point-like
defect 25 as well as between the point-like defect 26 and the
output waveguide 24, is Q.sub.in.about.3590; and .mu., the mutual
coupling coefficient between the point-like defects 25 and 26, is
.mu..about.-1.42.times.10.sup.-4 .omega..sub.0. From these values,
the coupling ratio is derived as 0.90, which falls within the
aforementioned preferable range: 0.2 to 10. Also, the resonance
wavelength .lamda..sub.0 of the point-like defects 25 and 26 is
1581.6 nm.
[0063] From these parameters, the multiplex/demultiplex spectrum of
the two-dimensional photonic crystal multiplexer/demultiplexer of
the present embodiment has been derived using the mode coupling
theory. For comparison, the same calculation has been conducted
also for the following two constructions: Comparative Example 1
(FIG. 7A): a two-dimensional photonic crystal
multiplexer/demultiplexer having only one point-like defect 31,
which construction corresponds to the present embodiment with one
of the point-like defects eliminated; and Comparative Example 2
(FIG. 7B): a two-dimensional photonic crystal
multiplexer/demultiplexer having only one point-like defect 32
equally spaced from both the input waveguide 23 and the output
waveguide 24 by a distance of (5/2).times.3.sup.0.5a. The results
of the calculations are shown in FIG. 8. The ordinate indicates the
multiplex/demultiplex spectrum I(.lamda.) in decibels:
I.sub.dB=10.times.log[I(.lamda.)/I(.lamda..sub.0)]. The
multiplex/demultiplex spectrum 40 of the present embodiment has the
following features: (i) Within the range in the proximity of
.lamda..sub.0, the multiplex/demultiplex spectrum of the present
embodiment takes larger values than the comparative examples,
showing a flattop shape. For example, the wavelength range where
I.sub.dB is equal to or larger than -1 dB (i.e.
I(.lamda.).about.0.79I(.lamda..sub.0)) is 0.25 nm for the
multiplex/demultiplex spectrum 41 of Comparative Example 1, 0.45 nm
for the multiplex/demultiplex spectrum 42 of Comparative Example 2,
and 0.43 nm for the present embodiment, which is larger than the
value of Comparative Example 1. Therefore, even if the resonance
wavelength .lamda..sub.0 is displaced from the original value due
to an error of a light generator or some other factor, the loss is
smaller in the present embodiment than in Comparative Example 1.
(ii) At any wavelength about 0.4 nm or more away from the resonance
wavelength .lamda..sub.0, the multiplex/demultiplex spectrum takes
a smaller value in the present embodiment than in any other
comparative examples, showing a shorter tail. The wavelength range
where I.sub.dB equals to -20 dB (i.e.
I(.lamda.).about.0.01I(.lamda..sub.0)) is 2.01 nm wide in the
present embodiment; this width is smaller than 4.8 nm of
Comparative Example 1 or 9.2 nm of Comparative Example 2. Thus,
compared to the other examples, the construction of the present
embodiment can reduce the noise caused by signals within the
wavelength range far from the resonance wavelength .lamda..sub.0
and suppress the crosstalk with signals from other channels.
[0064] The above-described calculation method using the mode
coupling theory is advantageous in that the multiplex/demultiplex
spectrum can be derived using function formulae. However, the
method is easily affected by an error in Q-value or mutual coupling
coefficient .mu.. Therefore, additional calculations have been
conducted using the FDTD method, which numerically determines the
multiplex/demultiplex spectrum without computing the Q-value or
.mu.. The result is as shown in FIG. 9 by filled circles. Though
the multiplex/demultiplex spectrum obtained is narrower than that
calculated using the mode coupling theory, it also shows a flattop
shape at around the resonance wavelength .lamda..sub.0 and a short
tail stretched over the wavelength range far from the resonance
wavelength .lamda..sub.0, as in the result of the calculation using
the mode coupling theory.
[0065] In addition, the multiplex/demultiplex spectrum has been
calculated using the FDTD method for the case where the point-like
defect 26 is shifted in the direction perpendicular to the
waveguide by (7/2).times.3.sup.0.5a and in the longitudinal
direction of the waveguide by 1.5a with respect to the point-like
defect 25. The result is as shown in FIG. 9 by triangles. The two
sets of data shown in FIG. 9 suggests that the construction of FIG.
10 having larger values at around the resonance wavelength is
preferable if the discrepancy of the resonance wavelength
.lamda..sub.0 is regarded as more important, whereas the
construction of FIG. 5 is recommendable if the suppression of the
noise or crosstalk is more important.
[0066] In the embodiment above, the optical output section of the
demultiplexer is constructed as the output waveguide 24. It is also
possible to construct it as a point-like defect. This point-like
defect also functions as the input section of a multiplexer. In the
example shown in FIG. 11, the output section of the demultiplexer
(or the input section of the multiplexer) consists of a point-like
defect 51 formed by omitting three holes 22 lying on a line,
similar to the point-like defects 25 and 26. The holes closest to
the point-like defect 51 are arranged at positions closer to the
corresponding triangular lattice points than in the case of the
point-like defects 25 and 26. This arrangement makes the Q-value of
the point-like defect 51 smaller than that of the point-like defect
25 or 26. The light extracted from the input waveguide 23 is
transmitted through the point-like defects 25 and 26 and emitted
from the body surface of the point-like defect 51 having the
reduced Q-value to the outside of the crystal.
[0067] The two-dimensional photonic crystal
multiplexer/demultiplexer according to the present invention can
take various forms: the point-like defect may be differently
shaped, such as a hole having a different diameter; and the holes
may be arranged in a different cyclic pattern, such as a square
lattice pattern.
[0068] FIG. 12 shows an embodiment of the two-dimensional photonic
crystal multiplexer/demultiplexer provided with reflecting sections
at the first and second optical input/output sections,
respectively, and having a heterostructure. The body 61 consists of
two forbidden band zones 63 and 64. The input waveguide 65 and the
output waveguide 66, which are identically shaped, pass through the
two forbidden band zones 63 and 64. The cycle of the holes 62 is
a.sub.1 for the forbidden band zone 63 and a.sub.2 for the
forbidden band zone 64, where a.sub.1>a.sub.2. Two point-like
defects 67 and 68 having the same shape are located between the
input waveguide 65 and the output waveguide 66.
[0069] In this construction, the transmission wavelength band of
the waveguide in the two forbidden band zones is as shown in FIG.
13. The input waveguide 65 and the output waveguide 66 have the
same transmission wavelength band because they are identically
shaped. The difference in cycle between the forbidden band zones 63
and 64 produces a wavelength band 75 that is included within the
transmission wavelength band 73 of the waveguide in the forbidden
band zone 63 but not within the transmission wavelength band 74 of
the waveguide in the forbidden band zone 64. The two cycles can be
appropriately determined so that the resonance wavelength of the
point-like defects 67 and 68 falls within the wavelength band 75.
In this construction, the light having the resonance wavelength and
propagating through the input waveguide 65 is reflected at the
boundary between the forbidden band zones 63 and 64. A ray of light
having the resonance wavelength that has passed by the point-like
defects 67 and 68 without being introduced into them is reflected
back and introduced into the point-like defects 67 and 68. Thus,
the demultiplexing efficiency is enhanced. Similarly, if a
demultiplexed ray of light is introduced through the point-like
defects 67 and 68 into the output waveguide 66, the light is
reflected at the boundary between the forbidden band zones 63 and
64 and extracted from only one end of the output waveguide 66. This
also contributes to the enhancement of the demultiplexing
efficiency.
* * * * *